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165-GHz Transceiver in SiGe Technology - Computer Engineering ...

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1090 IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 43, NO. 5, MAY 2008<br />

Fig. 7. Quadrature oscillator schematic.<br />

Odd mode:<br />

Quadrature mode:<br />

F<strong>in</strong>ally, (7) describes the quadrature oscillation condition and<br />

is obta<strong>in</strong>ed from <strong>in</strong>equalities (3), (4), and (5) and from (6), where<br />

is the negative resistance of the active device.<br />

It should be noted that, although the roles of and<br />

are not immediately apparent from the model of Fig. 5(a), they<br />

are critical <strong>in</strong> determ<strong>in</strong><strong>in</strong>g the phases of the oscillator outputs<br />

<strong>in</strong> a circuit implementation. S<strong>in</strong>ce the order of the entries of<br />

the quadrature-mode eigenvectors of (2) can be <strong>in</strong>terchanged<br />

without affect<strong>in</strong>g the solution, and are responsible<br />

for establish<strong>in</strong>g the exact phase relationships of the four outputs<br />

(i.e., which output is 0 , which is 90 , etc.). Furthermore,<br />

and help with suppress<strong>in</strong>g the odd and even oscillation<br />

modes by significantly degrad<strong>in</strong>g the of the capacitor <strong>in</strong><br />

Fig. 6(a) and (b).<br />

(4)<br />

(5)<br />

(6)<br />

(7)<br />

Fig. 8. Layout detail of the quadrature oscillator.<br />

Based on the concepts described above, the oscillator shown<br />

<strong>in</strong> Fig. 7 was designed for quadrature operation at a fundamental<br />

frequency of 80 <strong>GHz</strong>. S<strong>in</strong>ce AMOS varactors were not available<br />

<strong>in</strong> this technology, the oscillator was designed to operate<br />

at a constant frequency. However, more recent work <strong>in</strong> CMOS<br />

[15] illustrates that it is straightforward to extend this oscillator<br />

to a voltage-tunable version. In this design, the load resistor<br />

(of Fig. 5(a), where the fourth-harmonic signal is produced, is<br />

implemented with the bias resistors and . Cascode<br />

transistors are employed to adequately isolate the quadrature<br />

outputs from the tank. They also allow comb<strong>in</strong><strong>in</strong>g the two differential<br />

80-<strong>GHz</strong> signals <strong>in</strong>to two second-harmonic signals at<br />

160 <strong>GHz</strong> that are 180 out of phase.<br />

All transistors <strong>in</strong> the oscillator are biased at the peakcurrent<br />

density of 14 mA/ m to obta<strong>in</strong> the maximum output<br />

sw<strong>in</strong>g. Particular attention was paid to the symmetry of the oscillator<br />

layout, both for differential and for quadrature signals,<br />

as is illustrated <strong>in</strong> Fig. 8. The oscillator operates from 3.3 V, and

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